- Email: [email protected]
Magnetic sensorless control experiment without drift problem on HT-7
Fusion Engineering and Design 81 (2006) 1607–1612
Magnetic sensorless control experiment without drift problem on HT-7 K. Nakamura a,∗ , J.R. Luo b , H.Z. Wang b , Z.S. Ji b , H. Wang b , F. Wang c , N. Qi b , K.N. Sato a , K. Hanada a , M. Sakamoto a , H. Idei a , M. Hasegawa a , A. Iyomasa a , S. Kawasaki a , H. Nakashima a , A. Higashijima a a
Research Institute for Applied Mechanics, Kyushu University, Kasuga City, Fukuoka 816-8580, Japan Institute of Plasma Physics, Chinese Academy of Sciences, P.O. Box 1126, Hefei 230031, PR China Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga City, Fukuoka 816-8580, Japan b
c
Received 1 February 2005; received in revised form 8 August 2005; accepted 8 August 2005 Available online 10 January 2006
Abstract Magnetic sensorless control experiments of the plasma horizontal position have been carried out in the superconducting tokamak HT-7. Previously the horizontal position was calculated from the vertical field coil current and voltage without using signals of magnetic sensors like magnetic coils and flux loops placed near the plasma. The calculations are made focusing on the ripple frequency component of the power supply with thyristor and directly from them without time integration. There is no drift problem of integrator of magnetic sensors. Two kinds of experiments were carried out, to keep the position constant and swing the position in a triangular waveform. © 2005 Elsevier B.V. All rights reserved. Keywords: Sensorless control; Drift problem; HT-7
1. Introduction In a nuclear fusion reactor, diagnostic systems should be used for reactor protection and plasma control. Since the sensors are used under severe irradiation ∗ Corresponding author. Tel.: +81 92 583 7984; fax: +81 92 573 6899. E-mail address: [email protected] (K. Nakamura).
0920-3796/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.fusengdes.2005.08.094
circumstances, the number of diagnostic sensors placed near the plasma is desired to be small or zero and must not have a drift problem. Therefore, it is important to develop a sensorless control system in which there are no sensors of the controlled object and need no time integration. The sensorless control has been developed in two ways. For example, in a device with active magnetic bearings as actuators, the rotor displacement velocity was calculated from the voltage and current in the coil,
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K. Nakamura et al. / Fusion Engineering and Design 81 (2006) 1607–1612
and the displacement was obtained by integration [1]. On the other hand, in an active levitation control, the electromagnet is driven by a pulse width modulated (PWM) signal. The PWM carrier frequency component of the magnetic coil current is a function of the coil inductance. The gap between the electromagnet and the levitated object was calculated directly from the inductance without integration [2]. In this paper, we focus on the application to a plasma horizontal position control system, where the position is controlled by a vertical field coil. The voltage of the power supply for the vertical field coil is controlled by phase shift of the thyristor, and has ripples, whose frequency is higher than that of position controlling current. The ratio of the ripple frequency components of the coil voltage and current is a function of the coil inductance. The plasma horizontal position can be calculated directly from the inductance without integration. This sensing method has been applied to the superconducting tokamak HT-7, which presents severe conditions for magnetic sensorless sensing, since there is a thermal radiation shield between the plasma and the vertical field coil. This sensing method, however, is adequate to calculate the position after the shot. Therefore, the application to real-time plasma position control is studied and tried as the next step. In the superconducting tokamak HT-7 (the toroidal field Bt = 2.5 T, the major radius R = 1.22 m, the minor radius a = 0.26–0.30 m) of ASIPP [3], effect of eddy current in thermal radiation shield must be taken into account. The ratio of the ripple frequency (300 Hz) components of the vertical field coil voltage and current is calculated by Fourier expansion of the waveforms sampled every 0.1 for 3.3 ms before and after the time. We swept the plasma horizontal position at 7 Hz in the shot number 45 160. We calibrated the equivalent circuit parameters in the relation between the ratio and the plasma horizontal position by a least square method. Using these parameters, we calculated the x of the shot number 45 165 where the x was swept at a different frequency of 10 Hz. The calculated sinusoidal waveform of the x coincides with the one obtained from flux loop signal. The error is less than 2% of the plasma minor radius [1]. Using the equivalent circuit parameters calibrated above, feedback control of horizontal position was tested on HT-7 in 2004. Because of real-time control,
only past data for each one ripple period were used to calculate the position based on sensorless sensing. Two kinds of experiments were carried out, to keep the position constant and swing the position in a triangular waveform.
2. Experimental device and magnetic sensorless sensing principle The superconducting tokamak HT-7 has thermal radiation shields between the plasma and the superconducting toroidal field coil, and between the coil and the vertical field coil (Fig. 1). The shield acts as a stabilizing shell for plasma equilibrium and the position is measured by flux loops taking the shell effect into account. The plasma horizontal position is controlled by the vertical field coil power supply, where the phase of the thyristor is controlled at the frequency of 300 Hz. In a feedback control system of the plasma horizontal position xP , this is controlled by a vertical magnetic field made by vertical field coil current IV driven by the applied voltage VV . When the plasma shifts outward horizontally, a voltage is induced in the vertical field coil. In a voltage controlled power supply, IV is increased, and in a current controlled power supply, VV is reduced. Therefore, we can obtain some information on xP from the VV and IV , and we can deduce the xP from them.
Fig. 1. Cross-sectional view of poloidal field coil (squares), thermal radiation shields (broken circles), plasma and flux loops (circles) in the superconducting tokamak HT-7.
K. Nakamura et al. / Fusion Engineering and Design 81 (2006) 1607–1612
First, we consider the electrical equivalent circuit equations of the plasma (P), thermal radiation shield (S) and vertical field coil (V). Since the mutual inductances (M) between the plasma and the others depend on xP in the first-order approximation concerning elongation ratio and inverse aspect ratio: ΩP IP + s(LP IP ) + s(MPS IS ) + s(MPV IV ) = 0, IP
dMSP (sxP ) + MSP (sIP ) + (ΩS + sLS )IS dxP
+ MSV (sIV ) = 0,
(1)
(2)
dMVP IP (sxP ) + MVP (sIP ) + MVS (sIS ) dxP +(ΩV + sLV )IV = VV ,
(3)
where s is an operator for Laplace transformation, and L and Ω are inductance and resistance. By reducing IS from Eqs. (2) and (3), we can calculate (sxP ) from IP , IV and VV . Namely, the position speed (sxP ) is calculated directly but the time integration is necessary for deriving the position. The above principle can be applied to the ripple frequency (300 Hz) component of power supply current and voltage, neglecting the low-frequency component, i.e. the time derivative of xP (sxP ), the resistive voltage (ΩI), etc.: dLP dMPS LP + xP (sIP ) + MPS + xP (sIS ) dxP dxP dMPV + MPV + xP (sIV ) dxP = 0,
(4)
dMSP MSP + xP (sIP ) + LS (sIS ) + MSV (sIV ) = 0, dxP (5)
dMVP MVP + xP (sIP ) + MVS (sIS ) + LV (sIV ) dxP = VV .
(6)
By reducing IP and IS from these equations, the position (xP ) can be calculated directly from IV and VV , and the time integration is not necessary for deriving the position.
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The position is expressed as a fractional function of the ratio (VV /IV ). But this results from the above linearization, neglecting the low-frequency components to apply it finally for feedback control of plasma position, since high speed is necessary in detecting the plasma position. On the other hand, since high accuracy is also necessary, we improve it so that the position is expressed as a first-order lag element of the ratio. The amplitude of the voltage and current ripple is calculated from the fundamental Fourier component of each ripple. When voltage is constant, the phase difference between adjacent firing angles is equal to 120◦ , even if the voltage is different. This is similar to the case of PWM. When the voltage, however, increases, the phase difference between adjacent firing angles is less than 120◦ . And when the voltage decreases, the phase difference is greater than 120◦ . This point is a weak one compared with the case of PWM. Here the magnitude of the ripple frequency (300 Hz) component is defined as the magnitude of the fundamental Fourier component. The Fourier transformation is made maximum near the frequency for every period. Last, calculation of the lag element of a first order is made by digital integration on an analogue computer. The time resolution of the plasma horizontal position measurement based on magnetic sensorless sensing is limited by the ripple frequency as well as that obtained from the flux loop signal.
3. Experimental results of magnetic sensorless sensing and discussions In the superconducting tokamak HT-7, the effect of eddy current in the thermal radiation shield must be taken into account. The plasma horizontal position is swept horizontally (the amplitude is smaller than 1 cm) at 7 Hz in the shot number 45 160. Since IS is not measured, we cannot determine the mutual inductances, MPS between the plasma and the shield, and MSV between the shield and the vertical field coil separately. We can determine only the effective mutual inductance (MPV − MPS MSV /LS ) between the plasma and the vertical field coil. The ratio of the ripple frequency (300 Hz) components of the vertical field coil voltage and current is calculated by Fourier transformation of the waveforms
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K. Nakamura et al. / Fusion Engineering and Design 81 (2006) 1607–1612
sampled every 0.1 ms. From Eqs. (4)–(6), the ratio is expressed as a fractional function of xP . But practically a first-order transfer function should be sufficient to take into account the resistive effect. The relation between the ratio (impedance) and the plasma horizontal position is calibrated from the waveform of the shot number 45 160 from 200 to 800 ms, i.e. the gain and time constant of the lag element, and the pedestal are determined. Using these parameters, we applied this method to evaluate xP in the shot number 45 165 where xP was swept at the different frequency of 10 Hz. The calibrated relation is applied to this shot number 45 165. The error of the derived plasma position is lower than 2% of the plasma minor radius, and only the calculated position in the first cycle just after 200 ms depends on the starting position [4]. Although the error amount of 2% is sufficient with respect to the required accuracy of the plasma position control, it may be too high with respect to the SOL and with respect to the position of the x-point near the divertor. But the waveforms of the divertor coil current and voltage would give more information on them, especially on the position of the x-point, and the error amount would decrease.
4. Experimental results of magnetic sensorless control and discussions In the magnetic sensorless sensing, we have made analysis of the data from HT-7 off-line. In order to apply the magnetic sensorless sensing method to feedback control of plasma position, we must take into account the real-time processing, the noise rejection, the accuracy and the calculation time. The pre-processing for extracting the ripple component is necessary before the calculation of the fundamental Fourier component. In the real-time control system, only the past data are available in reducing the low-frequency component and the high frequency noise from the raw current signal. The time lag due to the past data should be compensated by adjusting the time constant of the first-order lag element. The phase of the ripple depends on the firing angle. The amplitude of the current ripple is very small, although that of the voltage ripple is large. The current
ripple depends on the frequency. The ratio of the current ripple to the main current of low-frequency (almost DC) component is about 0.3%. The small current ripple changes according to the plasma shift via change in the effective mutual inductance. The current ripple changes by 0.2% per plasma shift of 10 mm. Consequently, the current ripple should be amplified beforehand, so that the plasma displacement dependence on the ripple component could be detected clearly with 16-bit AD converter. Using the equivalent circuit parameters calibrated above, feedback control of horizontal position was tested on HT-7 in 2004. Because of real-time control, only past data for each one ripple period were used to calculate the position based on sensorless sensing. In the first experiment to keep the position constant, it goes inward linearly in time as shown in Fig. 2. In the second to swing the position in a triangular waveform, it follows outward shift well, but does not inward one as shown in Fig. 3. The asymmetric behavior suggests an asymmetric cause of sensorless sensing. It may be caused by increase in the ripple frequency as the phase-controlled voltage increases. In this control experiment, however, the calculation of the fundamental Fourier component and the pre-processing for extracting the ripple component were made by fixing the period of the thyristor ripple for simplicity. The easiest way for adjusting the variable period is to input the command signal for constant-voltage control of the power supply for vertical field coil and calculate the period from the time derivative. We should endeavor on making the calculation fast without decreasing the accuracy. Neural network (multilayer perceptron) could shorten the time, although it takes much time for the training.
5. Summary Sensorless sensing experiments were carried out in the superconducting tokamak HT-7. The plasma horizontal position was estimated from the vertical field coil current and voltage. The plasma horizontal position was directly calculated from the ratio of the fundamental Fourier components of the voltage and the current without time integration. Therefore, this technique is very advantageous for the application to long
K. Nakamura et al. / Fusion Engineering and Design 81 (2006) 1607–1612
Fig. 2. The first experiment to keep the position constant based on sensorless control. IP : plasma current, IV : vertical field coil current, VV : vertical field voltage, xSL : plasma position based on sensorless sensing, xFL : plasma position deduced from flux loop signal. Although xSL is almost constant by feedback control, xFL goes inward linearly.
pulse tokamak discharges without suffering from the drift problem in time integration of magnetic signals. This method may be adopted as a position sensing one for feedback control, even in a nuclear fusion reactor. In the magnetic sensorless control experiment on HT-7, if the asymmetric cause of sensorless sensing were eliminated, the plasma position could be controlled stably based on magnetic sensorless sensing method under disturbances from other poloidal coils and thermal radiation shield. This sensorless control concept may be extended to the
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Fig. 3. The second experiment to swing the position in a triangular waveform according to flux loop signal. The notations are the same as in Fig. 2. Although xSL follows outward shift well, it does not inward one.
one of elongation, triangularity, and resistive wall mode. Acknowledgement This sensorless control work has been partially supported by JSPS-CAS Scientist Exchange Program. References [1] D. Vischer, H. Bleuler, A new approach to sensorless and voltage controlled AMBs based on network theory concepts, in: Proceedings of the Second Int. Symp. on Magnetic Bearing, Tokyo, 1990, pp. 301–306.
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K. Nakamura et al. / Fusion Engineering and Design 81 (2006) 1607–1612
[2] K. Matsuda, Y. Okada, Self-sensing magnetic levitation control by using the PWM driving method, J. Jpn. Soc. Appl. Electromagn. Mech. 3 (1995) 23–29. [3] Y. Wan, HT-7 Team, HT-7U Team, Overview of steady state operation of HT-7 and present status of the HT-7U project, Nucl. Fusion 40 (2000) 1057–1068.
[4] K. Nakamura, Z.S. Ji, B. Shen, P.J. Qin, S. Itoh, K. Hanada, M. Sakamoto, E. Jotaki, M. Hasegawa, A. Iyomasa, S. Kawasaki, H. Nakashima, Sensorless sensing of plasma horizontal position on HT-7, Fusion Eng. Des. 66–68 (2003) 771–777.
Magnetic sensorless control experiment without drift problem on HT-7 K. Nakamura a,∗ , J.R. Luo b , H.Z. Wang b , Z.S. Ji b , H. Wang b , F. Wang c , N. Qi b , K.N. Sato a , K. Hanada a , M. Sakamoto a , H. Idei a , M. Hasegawa a , A. Iyomasa a , S. Kawasaki a , H. Nakashima a , A. Higashijima a a
Research Institute for Applied Mechanics, Kyushu University, Kasuga City, Fukuoka 816-8580, Japan Institute of Plasma Physics, Chinese Academy of Sciences, P.O. Box 1126, Hefei 230031, PR China Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga City, Fukuoka 816-8580, Japan b
c
Received 1 February 2005; received in revised form 8 August 2005; accepted 8 August 2005 Available online 10 January 2006
Abstract Magnetic sensorless control experiments of the plasma horizontal position have been carried out in the superconducting tokamak HT-7. Previously the horizontal position was calculated from the vertical field coil current and voltage without using signals of magnetic sensors like magnetic coils and flux loops placed near the plasma. The calculations are made focusing on the ripple frequency component of the power supply with thyristor and directly from them without time integration. There is no drift problem of integrator of magnetic sensors. Two kinds of experiments were carried out, to keep the position constant and swing the position in a triangular waveform. © 2005 Elsevier B.V. All rights reserved. Keywords: Sensorless control; Drift problem; HT-7
1. Introduction In a nuclear fusion reactor, diagnostic systems should be used for reactor protection and plasma control. Since the sensors are used under severe irradiation ∗ Corresponding author. Tel.: +81 92 583 7984; fax: +81 92 573 6899. E-mail address: [email protected] (K. Nakamura).
0920-3796/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.fusengdes.2005.08.094
circumstances, the number of diagnostic sensors placed near the plasma is desired to be small or zero and must not have a drift problem. Therefore, it is important to develop a sensorless control system in which there are no sensors of the controlled object and need no time integration. The sensorless control has been developed in two ways. For example, in a device with active magnetic bearings as actuators, the rotor displacement velocity was calculated from the voltage and current in the coil,
1608
K. Nakamura et al. / Fusion Engineering and Design 81 (2006) 1607–1612
and the displacement was obtained by integration [1]. On the other hand, in an active levitation control, the electromagnet is driven by a pulse width modulated (PWM) signal. The PWM carrier frequency component of the magnetic coil current is a function of the coil inductance. The gap between the electromagnet and the levitated object was calculated directly from the inductance without integration [2]. In this paper, we focus on the application to a plasma horizontal position control system, where the position is controlled by a vertical field coil. The voltage of the power supply for the vertical field coil is controlled by phase shift of the thyristor, and has ripples, whose frequency is higher than that of position controlling current. The ratio of the ripple frequency components of the coil voltage and current is a function of the coil inductance. The plasma horizontal position can be calculated directly from the inductance without integration. This sensing method has been applied to the superconducting tokamak HT-7, which presents severe conditions for magnetic sensorless sensing, since there is a thermal radiation shield between the plasma and the vertical field coil. This sensing method, however, is adequate to calculate the position after the shot. Therefore, the application to real-time plasma position control is studied and tried as the next step. In the superconducting tokamak HT-7 (the toroidal field Bt = 2.5 T, the major radius R = 1.22 m, the minor radius a = 0.26–0.30 m) of ASIPP [3], effect of eddy current in thermal radiation shield must be taken into account. The ratio of the ripple frequency (300 Hz) components of the vertical field coil voltage and current is calculated by Fourier expansion of the waveforms sampled every 0.1 for 3.3 ms before and after the time. We swept the plasma horizontal position at 7 Hz in the shot number 45 160. We calibrated the equivalent circuit parameters in the relation between the ratio and the plasma horizontal position by a least square method. Using these parameters, we calculated the x of the shot number 45 165 where the x was swept at a different frequency of 10 Hz. The calculated sinusoidal waveform of the x coincides with the one obtained from flux loop signal. The error is less than 2% of the plasma minor radius [1]. Using the equivalent circuit parameters calibrated above, feedback control of horizontal position was tested on HT-7 in 2004. Because of real-time control,
only past data for each one ripple period were used to calculate the position based on sensorless sensing. Two kinds of experiments were carried out, to keep the position constant and swing the position in a triangular waveform.
2. Experimental device and magnetic sensorless sensing principle The superconducting tokamak HT-7 has thermal radiation shields between the plasma and the superconducting toroidal field coil, and between the coil and the vertical field coil (Fig. 1). The shield acts as a stabilizing shell for plasma equilibrium and the position is measured by flux loops taking the shell effect into account. The plasma horizontal position is controlled by the vertical field coil power supply, where the phase of the thyristor is controlled at the frequency of 300 Hz. In a feedback control system of the plasma horizontal position xP , this is controlled by a vertical magnetic field made by vertical field coil current IV driven by the applied voltage VV . When the plasma shifts outward horizontally, a voltage is induced in the vertical field coil. In a voltage controlled power supply, IV is increased, and in a current controlled power supply, VV is reduced. Therefore, we can obtain some information on xP from the VV and IV , and we can deduce the xP from them.
Fig. 1. Cross-sectional view of poloidal field coil (squares), thermal radiation shields (broken circles), plasma and flux loops (circles) in the superconducting tokamak HT-7.
K. Nakamura et al. / Fusion Engineering and Design 81 (2006) 1607–1612
First, we consider the electrical equivalent circuit equations of the plasma (P), thermal radiation shield (S) and vertical field coil (V). Since the mutual inductances (M) between the plasma and the others depend on xP in the first-order approximation concerning elongation ratio and inverse aspect ratio: ΩP IP + s(LP IP ) + s(MPS IS ) + s(MPV IV ) = 0, IP
dMSP (sxP ) + MSP (sIP ) + (ΩS + sLS )IS dxP
+ MSV (sIV ) = 0,
(1)
(2)
dMVP IP (sxP ) + MVP (sIP ) + MVS (sIS ) dxP +(ΩV + sLV )IV = VV ,
(3)
where s is an operator for Laplace transformation, and L and Ω are inductance and resistance. By reducing IS from Eqs. (2) and (3), we can calculate (sxP ) from IP , IV and VV . Namely, the position speed (sxP ) is calculated directly but the time integration is necessary for deriving the position. The above principle can be applied to the ripple frequency (300 Hz) component of power supply current and voltage, neglecting the low-frequency component, i.e. the time derivative of xP (sxP ), the resistive voltage (ΩI), etc.: dLP dMPS LP + xP (sIP ) + MPS + xP (sIS ) dxP dxP dMPV + MPV + xP (sIV ) dxP = 0,
(4)
dMSP MSP + xP (sIP ) + LS (sIS ) + MSV (sIV ) = 0, dxP (5)
dMVP MVP + xP (sIP ) + MVS (sIS ) + LV (sIV ) dxP = VV .
(6)
By reducing IP and IS from these equations, the position (xP ) can be calculated directly from IV and VV , and the time integration is not necessary for deriving the position.
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The position is expressed as a fractional function of the ratio (VV /IV ). But this results from the above linearization, neglecting the low-frequency components to apply it finally for feedback control of plasma position, since high speed is necessary in detecting the plasma position. On the other hand, since high accuracy is also necessary, we improve it so that the position is expressed as a first-order lag element of the ratio. The amplitude of the voltage and current ripple is calculated from the fundamental Fourier component of each ripple. When voltage is constant, the phase difference between adjacent firing angles is equal to 120◦ , even if the voltage is different. This is similar to the case of PWM. When the voltage, however, increases, the phase difference between adjacent firing angles is less than 120◦ . And when the voltage decreases, the phase difference is greater than 120◦ . This point is a weak one compared with the case of PWM. Here the magnitude of the ripple frequency (300 Hz) component is defined as the magnitude of the fundamental Fourier component. The Fourier transformation is made maximum near the frequency for every period. Last, calculation of the lag element of a first order is made by digital integration on an analogue computer. The time resolution of the plasma horizontal position measurement based on magnetic sensorless sensing is limited by the ripple frequency as well as that obtained from the flux loop signal.
3. Experimental results of magnetic sensorless sensing and discussions In the superconducting tokamak HT-7, the effect of eddy current in the thermal radiation shield must be taken into account. The plasma horizontal position is swept horizontally (the amplitude is smaller than 1 cm) at 7 Hz in the shot number 45 160. Since IS is not measured, we cannot determine the mutual inductances, MPS between the plasma and the shield, and MSV between the shield and the vertical field coil separately. We can determine only the effective mutual inductance (MPV − MPS MSV /LS ) between the plasma and the vertical field coil. The ratio of the ripple frequency (300 Hz) components of the vertical field coil voltage and current is calculated by Fourier transformation of the waveforms
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K. Nakamura et al. / Fusion Engineering and Design 81 (2006) 1607–1612
sampled every 0.1 ms. From Eqs. (4)–(6), the ratio is expressed as a fractional function of xP . But practically a first-order transfer function should be sufficient to take into account the resistive effect. The relation between the ratio (impedance) and the plasma horizontal position is calibrated from the waveform of the shot number 45 160 from 200 to 800 ms, i.e. the gain and time constant of the lag element, and the pedestal are determined. Using these parameters, we applied this method to evaluate xP in the shot number 45 165 where xP was swept at the different frequency of 10 Hz. The calibrated relation is applied to this shot number 45 165. The error of the derived plasma position is lower than 2% of the plasma minor radius, and only the calculated position in the first cycle just after 200 ms depends on the starting position [4]. Although the error amount of 2% is sufficient with respect to the required accuracy of the plasma position control, it may be too high with respect to the SOL and with respect to the position of the x-point near the divertor. But the waveforms of the divertor coil current and voltage would give more information on them, especially on the position of the x-point, and the error amount would decrease.
4. Experimental results of magnetic sensorless control and discussions In the magnetic sensorless sensing, we have made analysis of the data from HT-7 off-line. In order to apply the magnetic sensorless sensing method to feedback control of plasma position, we must take into account the real-time processing, the noise rejection, the accuracy and the calculation time. The pre-processing for extracting the ripple component is necessary before the calculation of the fundamental Fourier component. In the real-time control system, only the past data are available in reducing the low-frequency component and the high frequency noise from the raw current signal. The time lag due to the past data should be compensated by adjusting the time constant of the first-order lag element. The phase of the ripple depends on the firing angle. The amplitude of the current ripple is very small, although that of the voltage ripple is large. The current
ripple depends on the frequency. The ratio of the current ripple to the main current of low-frequency (almost DC) component is about 0.3%. The small current ripple changes according to the plasma shift via change in the effective mutual inductance. The current ripple changes by 0.2% per plasma shift of 10 mm. Consequently, the current ripple should be amplified beforehand, so that the plasma displacement dependence on the ripple component could be detected clearly with 16-bit AD converter. Using the equivalent circuit parameters calibrated above, feedback control of horizontal position was tested on HT-7 in 2004. Because of real-time control, only past data for each one ripple period were used to calculate the position based on sensorless sensing. In the first experiment to keep the position constant, it goes inward linearly in time as shown in Fig. 2. In the second to swing the position in a triangular waveform, it follows outward shift well, but does not inward one as shown in Fig. 3. The asymmetric behavior suggests an asymmetric cause of sensorless sensing. It may be caused by increase in the ripple frequency as the phase-controlled voltage increases. In this control experiment, however, the calculation of the fundamental Fourier component and the pre-processing for extracting the ripple component were made by fixing the period of the thyristor ripple for simplicity. The easiest way for adjusting the variable period is to input the command signal for constant-voltage control of the power supply for vertical field coil and calculate the period from the time derivative. We should endeavor on making the calculation fast without decreasing the accuracy. Neural network (multilayer perceptron) could shorten the time, although it takes much time for the training.
5. Summary Sensorless sensing experiments were carried out in the superconducting tokamak HT-7. The plasma horizontal position was estimated from the vertical field coil current and voltage. The plasma horizontal position was directly calculated from the ratio of the fundamental Fourier components of the voltage and the current without time integration. Therefore, this technique is very advantageous for the application to long
K. Nakamura et al. / Fusion Engineering and Design 81 (2006) 1607–1612
Fig. 2. The first experiment to keep the position constant based on sensorless control. IP : plasma current, IV : vertical field coil current, VV : vertical field voltage, xSL : plasma position based on sensorless sensing, xFL : plasma position deduced from flux loop signal. Although xSL is almost constant by feedback control, xFL goes inward linearly.
pulse tokamak discharges without suffering from the drift problem in time integration of magnetic signals. This method may be adopted as a position sensing one for feedback control, even in a nuclear fusion reactor. In the magnetic sensorless control experiment on HT-7, if the asymmetric cause of sensorless sensing were eliminated, the plasma position could be controlled stably based on magnetic sensorless sensing method under disturbances from other poloidal coils and thermal radiation shield. This sensorless control concept may be extended to the
1611
Fig. 3. The second experiment to swing the position in a triangular waveform according to flux loop signal. The notations are the same as in Fig. 2. Although xSL follows outward shift well, it does not inward one.
one of elongation, triangularity, and resistive wall mode. Acknowledgement This sensorless control work has been partially supported by JSPS-CAS Scientist Exchange Program. References [1] D. Vischer, H. Bleuler, A new approach to sensorless and voltage controlled AMBs based on network theory concepts, in: Proceedings of the Second Int. Symp. on Magnetic Bearing, Tokyo, 1990, pp. 301–306.
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K. Nakamura et al. / Fusion Engineering and Design 81 (2006) 1607–1612
[2] K. Matsuda, Y. Okada, Self-sensing magnetic levitation control by using the PWM driving method, J. Jpn. Soc. Appl. Electromagn. Mech. 3 (1995) 23–29. [3] Y. Wan, HT-7 Team, HT-7U Team, Overview of steady state operation of HT-7 and present status of the HT-7U project, Nucl. Fusion 40 (2000) 1057–1068.
[4] K. Nakamura, Z.S. Ji, B. Shen, P.J. Qin, S. Itoh, K. Hanada, M. Sakamoto, E. Jotaki, M. Hasegawa, A. Iyomasa, S. Kawasaki, H. Nakashima, Sensorless sensing of plasma horizontal position on HT-7, Fusion Eng. Des. 66–68 (2003) 771–777.